Implement Merge Sort Problem Statement

Given a list of numbers, sort it using the Merge Sort algorithm.

Example

{
"arr": [5, 8, 3, 9, 4, 1, 7]
}

Output:

[1, 3, 4, 5, 7, 8, 9]

Notes

Constraints:

• 1 <= length of the given list <= 10⁵
• -10⁹ <= number in the list <= 10⁹

Explanation:
https://stg.interviewkickstart.com /blogs/learn/merge-sort

Implement Merge Sort Solution 1: Iterative

Code For Implement Merge Sort Solution 1: Iterative

    /*
    Asymptotic complexity in terms of size of `arr` `n`:
    * Time: O(n * log(n)).
    * Auxiliary space: O(n).
    * Total space: O(n).
    */
    static ArrayList<Integer> merge_sort(ArrayList<Integer> arr) {
        int n = arr.size();
        int left = 0, right = n - 1;
        split(arr, left, right);
        return arr;
    }

    static void split(List<Integer> arr, int l, int h) {
        // divide the array into blocks of size [1, 2, 4, 8, ..]
        for (int blocks = 1; blocks <= h - l; blocks = 2 * blocks) {
            // for blocks = 1, i = 0, 2, 4, 6, 8 and so on
            // for each block we split the array into sub arrays and merge them
            /* note that each of these subarrays will always be sorted as we are
             building the array from smaller subarrays to larger subarrays*/
            for (int i = l; i < h; i += 2 * blocks) {
                int left = i;
                int mid = Math.min(i + blocks - 1, h);
                int right = Math.min(i + 2 * blocks - 1, h);
                merge(arr, left, mid, right);
            }
        }
    }

    /*function to merge 2 sorted arrays*/
    static void merge(List<Integer> arr, int left, int mid, int right) {
        int[] l = new int[mid - left + 1];
        //copies the integers to array l from arr
        for(int i = 0; i < mid - left + 1; i++) {
            l[i] = arr.get(left + i);
        }
        int[] r = new int[right - mid];
        //copies the integers to array r from arr
        for(int i = 0; i < right - mid; i++) {
            r[i] = arr.get(mid + i + 1);
        }
        int i = 0, j = 0, k = left;
        //merges arrays l and r back to arr
        while(i < l.length && j < r.length) {
            if(l[i] <= r[j]) {
                arr.set(k, l[i]);
                i++;
            }
            else {
                arr.set(k, r[j]);
                j++;
            }
            k++;
        }
        //merges remaining elements of arrays l and r
        while(i < l.length) {
            arr.set(k++, l[i++]);
        }
        while(j < r.length) {
            arr.set(k++, r[j++]);
        }
    }

Implement Merge Sort Solution 2: Recursive

Code For Implement Merge Sort Solution 2: Recursive

    /*
    Asymptotic complexity in terms of size of `arr` `n`:
    * Time: O(n * log(n)).
    * Auxiliary space: O(n).
    * Total space: O(n).
    */
    static ArrayList<Integer> merge_sort(ArrayList<Integer> arr) {
        int n = arr.size();
        int left = 0, right = n - 1;
        split(arr, left, right);
        return arr;
    }

    /*function to partition the array into subarrays and then merge them*/
    static void split(List<Integer> arr, int left, int right) {
        if(left < right) {
            int mid = (left + right) / 2;
            //sort first and second halves of the array
            split(arr, left, mid);
            split(arr, mid + 1, right);
            //merge the sorted halves
            merge(arr, left, mid, right);
        }
    }

    /*function to merge 2 sorted arrays*/
    static void merge(List<Integer> arr, int left, int mid, int right) {
        int[] l = new int[mid - left + 1];
        //copies the integers to array l from arr
        for(int i = 0; i < mid - left + 1; i++) {
            l[i] = arr.get(left + i);
        }
        int[] r = new int[right - mid];
        //copies the integers to array r from arr
        for(int i = 0; i < right - mid; i++) {
            r[i] = arr.get(mid + i + 1);
        }
        int i = 0, j = 0, k = left;
        //merges arrays l and r back to arr
        while(i < l.length && j < r.length) {
            if(l[i] <= r[j]) {
                arr.set(k, l[i]);
                i++;
            }
            else {
                arr.set(k, r[j]);
                j++;
            }
            k++;
        }
        //merges remaining elements of arrays l and r
        while(i < l.length) {
            arr.set(k++, l[i++]);
        }
        while(j < r.length) {
            arr.set(k++, r[j++]);
        }
    }

We hope that these solutions to merge sort problem have helped you level up your coding skills. You can expect problems like these at top tech companies like Amazon and Google.

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